Difference between revisions of "Ricker wavelet"

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:<math>A = (1-2 \pi^2 f^2 t^2) e^{-\pi^2 f^2 t^2} </math>
 
:<math>A = (1-2 \pi^2 f^2 t^2) e^{-\pi^2 f^2 t^2} </math>
  
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[[File:Ricker_wavelet.png|thumb|Example Ricker wavelet, as plotted by [http://www.wolframalpha.com/input/?i=minimize+%281-2*pi%5E2*25%5E2*x%5E2%29*e%5E%28-1*pi%5E2*25%5E2*x%5E2%29+for+-0.033+%3C+x+%3C+0.033 WolframAlpha] ]]
 
Sometimes the period (somewhat erroneously referred to occasionally as the wavelength) is given as 1/''f'', but since it has mixed frequencies, this is not quite correct, and for some wavelets is not even a good approximation. In fact, the Ricker wavelet has its sidelobe minima at  
 
Sometimes the period (somewhat erroneously referred to occasionally as the wavelength) is given as 1/''f'', but since it has mixed frequencies, this is not quite correct, and for some wavelets is not even a good approximation. In fact, the Ricker wavelet has its sidelobe minima at  
  

Revision as of 18:22, 29 June 2011

A model seismic wavelet.

The amplitude A of the Ricker wavelet with peak frequency f at time t is computed like so:

Example Ricker wavelet, as plotted by WolframAlpha

Sometimes the period (somewhat erroneously referred to occasionally as the wavelength) is given as 1/f, but since it has mixed frequencies, this is not quite correct, and for some wavelets is not even a good approximation. In fact, the Ricker wavelet has its sidelobe minima at

These minima have the value